An Introduction to Difference Equations

1. Front Matter

   Pages i-xiii

   PDF

2. Dynamics of First Order Difference Equations

   • Saber N. Elaydi

   Pages 1-48

3. Linear Difference Equations of Higher Order

   • Saber N. Elaydi

   Pages 49-111

4. Systems of Difference Equations

   • Saber N. Elaydi

   Pages 113-162

5. Stability Theory

   • Saber N. Elaydi

   Pages 163-220

6. The Z-Transform Method

   • Saber N. Elaydi

   Pages 221-257

7. Control Theory

   • Saber N. Elaydi

   Pages 259-302

8. Asymptotic Behavior of Difference Equations

   • Saber N. Elaydi

   Pages 303-349

9. Oscillation Theory

   • Saber N. Elaydi

   Pages 351-369

10. Back Matter

    Pages 371-390

    PDF

This book grew out of lecture notes I used in a course on difference equations that I taught at Trinity University for the past five years. The classes were largely pop­ ulated by juniors and seniors majoring in Mathematics, Engineering, Chemistry, Computer Science, and Physics. This book is intended to be used as a textbook for a course on difference equations at the level of both advanced undergraduate and beginning graduate. It may also be used as a supplement for engineering courses on discrete systems and control theory. The main prerequisites for most of the material in this book are calculus and linear algebra. However, some topics in later chapters may require some rudiments of advanced calculus. Since many of the chapters in the book are independent, the instructor has great flexibility in choosing topics for the first one-semester course. A diagram showing the interdependence of the chapters in the book appears following the preface. This book presents the current state of affairs in many areas such as stability, Z-transform, asymptoticity, oscillations and control theory. However, this book is by no means encyclopedic and does not contain many important topics, such as Numerical Analysis, Combinatorics, Special functions and orthogonal polyno­ mials, boundary value problems, partial difference equations, chaos theory, and fractals. The nonselection of these topics is dictated not only by the limitations imposed by the elementary nature of this book, but also by the research interest (or lack thereof) of the author.

• Mathematica
• difference equation
• stability

• Department of Mathematics, Trinity University, San Antonio, USA

  Saber N. Elaydi

Policies and ethics